Double-layer potentials for a generalized bi-axially symmetric Helmholtz equation II

In earlier papers, the double-layer potential has been successfully applied in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known [Complex Var Elliptic Equ. 2007;52(8):673-683], while the potential theory was constructed only for the first one [Sohag J Math. 2015;2(1):1-10]. Here, in this paper, our goal is to construct theory of double-layer potentials corresponding to the next fundamental solution. We used some properties of one of Appell's hypergeometric functions with respect to two variables to prove the limiting theorems, while integral equations concerning the denseness of double-layer potentials are derived.